Finite Group Databasebeta

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C22×(C2×D167)⋊C4 #24923716

order10688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D167)⋊C4

Splittings

FittingC23×C4×C167 ⋊ C2
SylowC167 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D167
commutatorC2×C167C23×C4
FrattiniC22C23×D167
FittingC23×C4×C167C2
socleC24×C167C22
prime radicalC24×D167C2
cosocleC22×C167C24
hypercenterC23×C4D167
hypocenterC167C22×C22⋊C4
LCSG ▷ C2×C167 ▷ C167
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2696 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of(C2×D167)⋊#95, #36322374, #36322376, …
maximal normal subgroup of(C2×D167)⋊#95, #36322374, #36322376, …
maximal quotient ofC22×C167⋊#95, C2×C4×(C2×D167)⋊C4, C2×#24923124, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10688, 996);